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Only 3 lines? (Posted on 2005-07-14) Difficulty: 2 of 5
It is well-known the solution to the problem of connecting nine dots, arranged in three rows of 3 dots, with four straight lines, without lifting up the pencil from the paper where they are drawn, and without any tricks at all, like folding the paper, etc...
           o        o        o


           o        o        o


           o        o        o
The question is: given the nine dots above, is it possible to connect them with only 3 straight lines ? The restrictions are the same, that is, without lifting up the pencil from the paper where they are drawn, no tricks allowed, and if you retrace a line, you must count one more line.

Prove your answer!

Note: this is a revisit to the problem Nine Dots already posted in this site and you can use that drawing for reference.

See The Solution Submitted by pcbouhid    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 6 of 12 |
(In reply to Solution by Brian Smith)

The term "straight line" would seem to imply Euclidean geometry.  "Great circle" would be the spherical equivalent, or "geodesic" in a more general setting. Non-Euclidean geometry, at least beyond  spherical geometry, is probably outside the scope of perplexus. And for this problem, I would consider ringing in spherical geometry to be a trick.

  Posted by Richard on 2005-07-15 02:51:47

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